RSA Starter 1 — CryptoHack

Challenge

The most important operation in RSA is modular exponentiation: compute $a^b \mod n$. Submit the result of $101^{17} \mod 22663$.

Math

By definition, modular exponentiation is just repeated multiplication reduced after each step:

In practice we use square-and-multiply so even huge exponents stay tractable. For this challenge the numbers are small enough that any direct method works.

Solve

pow(101, 17, 22663)
# 19906

Python's three-argument pow(base, exp, mod) is the canonical primitive — it's the same one you'll reach for in every later RSA challenge.

Why this is the starting line

Every subsequent CryptoHack RSA challenge composes this primitive:

• Encrypt $c = m^e \bmod n$
• Decrypt $m = c^d \bmod n$
• Sign / verify are the same operations with different keys

If you can call pow(a, b, n) you can already do all of those — the rest of the series is about discovering when the math leaks (small $e$, shared $n$, reused nonces, low $d$, partial known plaintext, …).